196 
Miscellanea 
on the machine. The i-esults are tabled beneath the values of A^t/),^, or these are <\>i^. Put each 
on the calculator and multiply it by the row These products are given as the fifth 
figure in each constituent. The sixth figure is jVnpJ{7ipng) or is the result of dividing the first 
figure by the second. The seventh figure is the sixth multiplied by the fourth or 
and the eighth is the sixth figure multiplied by the fifth 
Itp Itq 
These are added up for each row and placed as the third and fourth figures in the N^(pq* 
column : added up for the column and divided by JV, they give 
WW^pJinpn,)} = -2444,586, 
which determine the first and second sums in the value of ^V^^. But 
= (-09580) + mSpg W)} : 
whence it follows that mS,,^ {Vp<iK'''^pK)) = -HSGS/.V, 
while <p''IN=Spq{4>\,)IN = -09580/^7 
is less in value. Thus the cubic terms in the contingency are more important than the square, 
and cannot in this case be neglected compared to them in the present case. 
Again ,S,,{iV,^/<^,2.W(''i>V} = '^>' + ^V2>S^,('^^^A: 
\ '*f) "■q J 
1 AT<i (A. "A, 2, 1/ M -0140827 -(-09580)2 
whence NS^ {(j),,- ^,'*x|',V(W;, '*,)} = 
= •00490/^^, 
while Sp,{<l)/(jig^)/iy=(f>yF= -00918/ K 
Thus the fifth order term is only one-half roughly of the fourth order term and is not in this case 
negligible with regard to it. It is clearly the very dull, very bad handwriters whose excess so 
emphasises these terms. In this, as in other cases, we cannot accordingly neglect any of the 
terms contributory to the probable error and we have by (xxxiii) : 
= ^ {-24446 + -00704 - -06718} = -^p^ , 
or, 0-^2= 1-9240/^= -001068, and o-^ = -0327*. 
But ffe = <r^/(l+(|)2)*, by (xxxv) 
- 1l-3l58l3i - 
Hence the probable error of C= -0192. 
The probable error of C, if it were found from the coefficient of correlation, would be 
•67449 (1 - »--2)/\/#= -0139. Thus the coefficient as found by mean squared contingency is rather 
more subject to error than the coefficient of correlation, say in the ratio of 4 to 3. The rule 
given in Pearson's memoir + appears, to judge by this case, to err on the side of asserting 
no significance, where after all it may exist. 
The actual arithmetic of determining the probable error is not so laborious as might have 
been anticipated. 
The coefficient of mean contingency obtained from the diagram in the memoir just cited is 
•31, so that it differs from C=-30 by less than the probable error. 
* Probable Error of ,^2 = -67449 x 200-^= -0042. 
t Drapers' Research Memoirs: Biometric Series, i., p. 18. Dulau <fe Co. 
